An infection forced doctors to amputate her right arm. The girl’s mother removed a tube that delivered medication to the girl’s heart, changed her clothes, and walked her out of the hospital Wednesday night.

‘‘If she contracts an infection, it really could just be a matter of days that could result in the young girl’s death,’’ Martos said. ‘‘It’s pretty serious.’’

Authorities had been stymied by health privacy laws that kept them from releasing the parents’ names, but police said Monday that US Border Patrol stopped the girl’s father, Luis Bracamontes, 46, as he crossed into Arizona from Mexico over the weekend.

Martos said the man provided no clues to the girl’s whereabouts and denied having any involvement in removing her from the hospital. Police released his name, along with that of the girl’s mother, Norma Bracamontes, 35, in hopes it will help locate the child.

Neither parent is charged with a crime yet, but authorities want the child brought back to the hospital before it is too late, Martos said.

He said the family lives a ‘‘nomadic’’ life without a permanent residence, but they have relatives in Arizona, California, and Mexico, none of whom have been able to provide police with information about their whereabouts.

The girl’s father is a Mexican citizen with a US resident alien identification card. The child and her mother are US citizens, Martos said.

Authorities do not know why the child’s parents took her from the hospital, but speculate they might have been concerned about paying the bill.